← Mechanical
Oscillation

Mass on a Spring

Pull a mass on a spring and release it — the cleanest example of simple harmonic motion.
Kinetic energy Spring potential energy Click a graph to read its value at that point
Show graphs:
Period T
0s
Frequency
0Hz
Max speed
0m/s
Damping
None
F = −k·x − c·v   |   T = 2π·√(m / k)   |   ω = √(k / m)
i About this experiment — click to learn the physics

What you're looking at

A block of mass m sits on a frictionless surface, attached to a wall by a spring. Pull it aside by an amount A and let go: the spring pulls it back, it overshoots, and it oscillates back and forth. This is the textbook example of simple harmonic motion (SHM) — the same mathematics behind clocks, atoms in a solid, and AC circuits.

Hooke's law and the restoring force

A spring pushes or pulls with a force proportional to how far it's stretched or compressed, always back toward equilibrium:

F = −k·x Hooke's law — the restoring force

Because the force is proportional to displacement (and opposite in direction), the motion is a perfect sinusoid: x(t) = A·cos(ωt). The lower trace on screen draws exactly this curve.

Period and frequency

The angular frequency and period depend only on the mass and stiffness — not on the amplitude. A bigger swing simply moves faster, taking the same time:

ω = √(k/m)  ·  T = 2π·√(m/k) independent of amplitude

A heavier mass oscillates more slowly; a stiffer spring oscillates faster. The maximum speed, reached as it flies through the centre, is v_max = A·ω.

Energy exchange

With no damping the total mechanical energy is conserved, sloshing between two forms — shown by the bar at the top:

  • Kinetic energy ½·m·v² peaks at the centre, where the block moves fastest.
  • Spring potential energy ½·k·x² peaks at the turning points, where the block is momentarily still.

Adding damping

Turn up the damping and a resistive force −c·v drains energy, so the oscillations shrink inside a decaying envelope. Push it far enough and the motion becomes critically damped (returns to rest as fast as possible without overshooting) or overdamped (creeps slowly back). Watch the regime label change as you raise c.